Probing the dark matter profile of hot clusters and the M-T relation with XMM-Newton

We present results based on XMM-Newton observations of a small sample of hot galaxy clusters. Making a full use of XMM-Newton's spectro-imaging capabilities, we have extracted the radial temperature profile and gas density profile, and with this information, calculated the total mass profile of each cluster (under the assumption of hydrostatic equilibrium and spherical symmetry). Comparing the individual scaled total mass profiles, we have probed the Universality of rich cluster mass profiles over a wide range of radii (from 0.01 to 0.7 the virial radius). We have also tested the shape of cluster mass profiles by comparing with the predicted profiles from numerical simulations of hierarchical structure formation. We also derived the local mass-temperature (M-T) scaling relation over a range of temperature going from 4 to 9 keV, that we compare with theoretical predictions.Comment: 7 pages, 2 figures, Advances in Space Research in press (proceedings of the COSPAR 2004 Assembly, Paris

Balancing Local Order and Long-Ranged Interactions in the Molecular Theory of Liquid Water

A molecular theory of liquid water is identified and studied on the basis of computer simulation of the TIP3P model of liquid water. This theory would be exact for models of liquid water in which the intermolecular interactions vanish outside a finite spatial range, and therefore provides a precise analysis tool for investigating the effects of longer-ranged intermolecular interactions. We show how local order can be introduced through quasi-chemical theory. Long-ranged interactions are characterized generally by a conditional distribution of binding energies, and this formulation is interpreted as a regularization of the primitive statistical thermodynamic problem. These binding-energy distributions for liquid water are observed to be unimodal. The gaussian approximation proposed is remarkably successful in predicting the Gibbs free energy and the molar entropy of liquid water, as judged by comparison with numerically exact results. The remaining discrepancies are subtle quantitative problems that do have significant consequences for the thermodynamic properties that distinguish water from many other liquids. The basic subtlety of liquid water is found then in the competition of several effects which must be quantitatively balanced for realistic results.Comment: 8 pages, 6 figure

Calibration of the galaxy cluster M_500-Y_X relation with XMM-Newton

The quantity Y_ X, the product of the X-ray temperature T_ X and gas mass M_ g, has recently been proposed as a robust low-scatter mass indicator for galaxy clusters. Using precise measurements from XMM-Newton data of a sample of 10 relaxed nearby clusters, spanning a Y_ X range of 10^13 -10^15 M_sun keV, we investigate the M_500-Y_ X relation. The M_500 - Y_ X data exhibit a power law relation with slope alpha=0.548 \pm 0.027, close to the self-similar value (3/5) and independent of the mass range considered. However, the normalisation is \sim 20% below the prediction from numerical simulations including cooling and galaxy feedback. We discuss two effects that could contribute to the normalisation offset: an underestimate of the true mass due to the HE assumption used in X-ray mass estimates, and an underestimate of the hot gas mass fraction in the simulations. A comparison of the functional form and scatter of the relations between various observables and the mass suggest that Y_ X may indeed be a better mass proxy than T_ X or M_g,500.Comment: 4 pages, 2 figures, accepted for publication in A&

Final state interactions in two-particle interferometry

We reconsider the influence of two-particle final state interactions (FSI) on two-particle Bose-Einstein interferometry. We concentrate in particular on the problem of particle emission at different times. Assuming chaoticity of the source, we derive a new general expression for the symmetrized two-particle cross section. We discuss the approximations needed to derive from the general result the Koonin-Pratt formula. Introducing a less stringent version of the so-called smoothness approximation we also derive a more accurate formula. It can be implemented into classical event generators and allows to calculate FSI corrected two-particle correlation functions via modified Bose-Einstein "weights".Comment: 12 pages RevTeX, 2 ps-figures included, submitted to Phys. Rev.

Tariff-Rate Quotas : Difficult to model or plain simple?

The difficulty of reliably and accurately incorporating tariffrate quotas (TRQs) into trade models has received a lot of attention in recent years. As a result of the Uruguay Round of GATT negotiations, TRQs replaced an assortment of tariff and nontariff instruments in an effort to standardise trade barriers, and facilitate their future liberalisation. Understanding the nuances of TRQs is now particularly crucial for New Zealand because of the preferential access arrangements that New Zealand has for a number of products in highly protected markets such as the European Union, Japan, and the United States. It has been argued that TRQs are complex instruments and are difficult to model because for any trade flow between two countries, one of three regimes may be applicable : 1. The import quota may not be binding and the within-quota tariff applies; 2. The quota may be binding, the within-quota tariff applies, and a quota rent is created; or 3. Trade occurs over and above the quota, in which case an over-quota tariff applies (although, even in this regime, someone is still able to collect the quota rent on within-quota trade). But even this characterisation, which many claim is too complex to model, is a major simplification of reality. Bilateral preferences are ubiquitous, and such preferences are usually included in the determination of multilateral market access quotas. It is usual, therefore, that the TRQ instrument has several tiers to the quota schedule, plus a number of within and over-quota tariff rates applicable on either a bilateral or a multilateral basis. Further trade liberalisation creates something of a dilemma for New Zealand. Any decrease in over-quota tariffs and/or increase in quota levels potentially reduces the value of quota rents, many of which accrue to New Zealand due to the bilateral preferences. It is important, therefore, that New Zealand trade negotiators understand how much additional trade is required to offset the loss of New Zealands quota rents. Modelling trade in the presence of TRQs is the only way to ascertain this knowledge. The purpose of this paper is to show that complex TRQs can be modelled very easily and precisely. The only catch is that the model must be formulated as a complementarity problem rather than the more conventional linear or nonlinear optimisation problem. The concept will be demonstrated using a simple 3-region, single commodity spatial price equilibrium model of trade.Tariff-rate quota, trade modelling, mathematical programming, complementarity

The hot gas content of fossil galaxy clusters

We investigate the properties of the hot gas in four fossil galaxy systems detected at high significance in the Planck Sunyaev-Zeldovich (SZ) survey. XMM-Newton observations reveal overall temperatures of kT ~ 5-6 keV and yield hydrostatic masses M500,HE > 3.5 x 10e14 Msun, confirming their nature as bona fide massive clusters. We measure the thermodynamic properties of the hot gas in X-rays (out to beyond R500 in three cases) and derive their individual pressure profiles out to R ~ 2.5 R500 with the SZ data. We combine the X-ray and SZ data to measure hydrostatic mass profiles and to examine the hot gas content and its radial distribution. The average Navarro-Frenk-White (NFW) concentration parameter, c500 = 3.2 +/- 0.4, is the same as that of relaxed `normal' clusters. The gas mass fraction profiles exhibit striking variation in the inner regions, but converge to approximately the cosmic baryon fraction (corrected for depletion) at R500. Beyond R500 the gas mass fraction profiles again diverge, which we interpret as being due to a difference in gas clumping and/or a breakdown of hydrostatic equilibrium in the external regions. Overall our observations point to considerable radial variation in the hot gas content and in the gas clumping and/or hydrostatic equilibrium properties in these fossil clusters, at odds with the interpretation of their being old, evolved and undisturbed. At least some fossil objects appear to be dynamically young.Comment: 4 pages, 2 figures. Accepted for publication in A&